I'm going on a big national car trip, and I want to increase cargo space by getting a roof rack, but I'm wondering how much the additional drag will increase my gas bill. Is there any way to figure this out?
A local newspaper here in Finland recently ran a fuel efficiency test that might provide some relevant data here. The original article is, alas, in Finnish only, but I'll summarize the results below.
The test compared the fuel consumption of the test vehicle (a Volvo V70 D4 diesel), on a test route that included both highway and urban driving, in three rooftop configurations. The results were:
Thus, the cargo box on the roof increased fuel consumption by about 5% compared to the baseline.
(The full test also measured the noise level at the driver's ear, and compared the ease of installation and various other aspects of the different options, but I'll leave those out of this summary. Suffice to say that the cargo box caused some steady but noticeable hum, and made the car somewhat more sensitive to side winds.)
ConsumerReports.org has done the analysis. Obviously it'll be different for every car and shape and size of roof rack, and contents of the rack, but in their experiment:
So that gives you an indication that it can add close to 50% to your fuel bill, depending on the load.
Short answer: It depends tremendously on who you ask and what vehicle is used.
An empty rack has been reported to increase the cost of fuel over time from anywhere from 1% to 15%, while a fully loaded roof rack will add 20% to 50% to your fuel bill. I'll justify these numbers below.
Note that however the exact same sources put the effect of "driving behaviors" at a shocking 35% - so the difference in calming down, using cruise control, and being in a relaxed travel mood while avoiding lane changes is about the same as putting on a roof rack and stuffing it full of bags, depending on your vehicle.
Methodology and citations below.
Sources: Consumer Reports - While this is reported in another answer, it solely uses MPG figures which are terribly bad for cross-comparison, and the empty-roof rack effect seemed so ridiculously high that it made me suspicious. Reports on different vehicles reported at little as a 1% reduction with an empty rack, so YMMV.
Edmunds.com - A multi-vehicle comparison with lots of assorted tests are run, and the data appears to be correctly interpretted into % savings.
Using a 2013 Honda Accord and data provided by Consumer Reports, an empty roof rack will increase the amount you spend on gas by 12% compared to no rack at all, assuming highway speeds. A two-bike rack with wind deflector will increase your gasoline costs by 36%. I am somewhat suspicious of this first figure, but it's possible.
Using a 2008 Buick Enclave with data from Edmunds, empty rails add only 1% to fuel costs but one suitcase and a cooler gave a 21% increase in fuel costs.
I very much like the Edmunds article for it's comparison of driving behavior, A/C usage vs rolling the windows down (verdict for the truck they tested: windows down better than A/C usage), however there still is little comparison amongst vehicles in the same conditions. In my 2010 Chevy Cobalt, for instance, I find A/C has an indiscernible effect on gas mileage possibly due to how the car is engineered, but this is not with scientific testing principles at all.
There appears to be a definite effect of loading luggage onto the roof of a car, and it is very likely in the neighborhood of 20-50% regardless of vehicle.
The reason is quite logical - the top of a vehicle is the worst possible place to put things, from an aerodynamic point of view. It tremendously adds to forward-facing surface area that directly hits the wind, it completely screws up the entire wind envelope for the rest of the vehicle, and it does this usually less than 1/3 of the distance into the length of the vehicle; you've basically completely thrown out all aerodynamic gains in the engineering of the entire vehicle, you might as well drive a giant cube.
On the other hand, what if you are already driving a big cube which isn't terribly aerodynamic to start with? Well, I just don't know, but I'm sure putting things on top will make it worse.
However, driving behavior can clearly have an effect as big as a roof rack, so don't stuff luggage inside the cab, annoy the inhabitants, and make yourself want to get there faster - you'll end up losing a lot of money that way!
As to exact or even more precise effects than this rather large range of 20-50%, it appears that bigger, heavier, stronger-engined vehicles are likely to show a smaller % change from roof-racks than smaller, more aerodynamic, lower-powered engine vehicles.
For short trips it probably won't matter, as your gas bill won't be all that high anyway...but if you are talking about a cross-country tour, that little roof rack can cost you a few hundred $ pretty quick.
Please remember that there are two different mpg's: US and UK. mpg is "miles per gallon" - unfortunately there are two different gallon sizes used, a US gallon of about 3.78 litres and an UK gallon ("imperial gallon") of 4.54 litres. As a result, the same car that does 50 mpg in the USA does 60 mpg in the UK.
Fuel consumption is made up of several components: Losses in the engine, rolling resistance, and wind resistance. The roof rack will mostly increase the wind resistance, and wind resistance grows enormously with speed, much more than rolling resistance. So a slight reduction in speed will reduce your loss of fuel efficiency a lot.